Polytope of Type {6,8,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,8,20}*1920a
Also Known As : {{6,8|2},{8,20|2}}. if this polytope has another name.
Group : SmallGroup(1920,148893)
Rank : 4
Schlafli Type : {6,8,20}
Number of vertices, edges, etc : 6, 24, 80, 20
Order of s0s1s2s3 : 120
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,4,20}*960, {6,8,10}*960
   3-fold quotients : {2,8,20}*640a
   4-fold quotients : {6,2,20}*480, {6,4,10}*480
   5-fold quotients : {6,8,4}*384a
   6-fold quotients : {2,4,20}*320, {2,8,10}*320
   8-fold quotients : {3,2,20}*240, {6,2,10}*240
   10-fold quotients : {6,4,4}*192, {6,8,2}*192
   12-fold quotients : {2,2,20}*160, {2,4,10}*160
   15-fold quotients : {2,8,4}*128a
   16-fold quotients : {3,2,10}*120, {6,2,5}*120
   20-fold quotients : {6,2,4}*96, {6,4,2}*96a
   24-fold quotients : {2,2,10}*80
   30-fold quotients : {2,4,4}*64, {2,8,2}*64
   32-fold quotients : {3,2,5}*60
   40-fold quotients : {3,2,4}*48, {6,2,2}*48
   48-fold quotients : {2,2,5}*40
   60-fold quotients : {2,2,4}*32, {2,4,2}*32
   80-fold quotients : {3,2,2}*24
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) : 
s0 := (  1,121)(  2,122)(  3,123)(  4,124)(  5,125)(  6,131)(  7,132)(  8,133)
(  9,134)( 10,135)( 11,126)( 12,127)( 13,128)( 14,129)( 15,130)( 16,136)
( 17,137)( 18,138)( 19,139)( 20,140)( 21,146)( 22,147)( 23,148)( 24,149)
( 25,150)( 26,141)( 27,142)( 28,143)( 29,144)( 30,145)( 31,151)( 32,152)
( 33,153)( 34,154)( 35,155)( 36,161)( 37,162)( 38,163)( 39,164)( 40,165)
( 41,156)( 42,157)( 43,158)( 44,159)( 45,160)( 46,166)( 47,167)( 48,168)
( 49,169)( 50,170)( 51,176)( 52,177)( 53,178)( 54,179)( 55,180)( 56,171)
( 57,172)( 58,173)( 59,174)( 60,175)( 61,181)( 62,182)( 63,183)( 64,184)
( 65,185)( 66,191)( 67,192)( 68,193)( 69,194)( 70,195)( 71,186)( 72,187)
( 73,188)( 74,189)( 75,190)( 76,196)( 77,197)( 78,198)( 79,199)( 80,200)
( 81,206)( 82,207)( 83,208)( 84,209)( 85,210)( 86,201)( 87,202)( 88,203)
( 89,204)( 90,205)( 91,211)( 92,212)( 93,213)( 94,214)( 95,215)( 96,221)
( 97,222)( 98,223)( 99,224)(100,225)(101,216)(102,217)(103,218)(104,219)
(105,220)(106,226)(107,227)(108,228)(109,229)(110,230)(111,236)(112,237)
(113,238)(114,239)(115,240)(116,231)(117,232)(118,233)(119,234)(120,235)
(241,361)(242,362)(243,363)(244,364)(245,365)(246,371)(247,372)(248,373)
(249,374)(250,375)(251,366)(252,367)(253,368)(254,369)(255,370)(256,376)
(257,377)(258,378)(259,379)(260,380)(261,386)(262,387)(263,388)(264,389)
(265,390)(266,381)(267,382)(268,383)(269,384)(270,385)(271,391)(272,392)
(273,393)(274,394)(275,395)(276,401)(277,402)(278,403)(279,404)(280,405)
(281,396)(282,397)(283,398)(284,399)(285,400)(286,406)(287,407)(288,408)
(289,409)(290,410)(291,416)(292,417)(293,418)(294,419)(295,420)(296,411)
(297,412)(298,413)(299,414)(300,415)(301,421)(302,422)(303,423)(304,424)
(305,425)(306,431)(307,432)(308,433)(309,434)(310,435)(311,426)(312,427)
(313,428)(314,429)(315,430)(316,436)(317,437)(318,438)(319,439)(320,440)
(321,446)(322,447)(323,448)(324,449)(325,450)(326,441)(327,442)(328,443)
(329,444)(330,445)(331,451)(332,452)(333,453)(334,454)(335,455)(336,461)
(337,462)(338,463)(339,464)(340,465)(341,456)(342,457)(343,458)(344,459)
(345,460)(346,466)(347,467)(348,468)(349,469)(350,470)(351,476)(352,477)
(353,478)(354,479)(355,480)(356,471)(357,472)(358,473)(359,474)(360,475)
(481,601)(482,602)(483,603)(484,604)(485,605)(486,611)(487,612)(488,613)
(489,614)(490,615)(491,606)(492,607)(493,608)(494,609)(495,610)(496,616)
(497,617)(498,618)(499,619)(500,620)(501,626)(502,627)(503,628)(504,629)
(505,630)(506,621)(507,622)(508,623)(509,624)(510,625)(511,631)(512,632)
(513,633)(514,634)(515,635)(516,641)(517,642)(518,643)(519,644)(520,645)
(521,636)(522,637)(523,638)(524,639)(525,640)(526,646)(527,647)(528,648)
(529,649)(530,650)(531,656)(532,657)(533,658)(534,659)(535,660)(536,651)
(537,652)(538,653)(539,654)(540,655)(541,661)(542,662)(543,663)(544,664)
(545,665)(546,671)(547,672)(548,673)(549,674)(550,675)(551,666)(552,667)
(553,668)(554,669)(555,670)(556,676)(557,677)(558,678)(559,679)(560,680)
(561,686)(562,687)(563,688)(564,689)(565,690)(566,681)(567,682)(568,683)
(569,684)(570,685)(571,691)(572,692)(573,693)(574,694)(575,695)(576,701)
(577,702)(578,703)(579,704)(580,705)(581,696)(582,697)(583,698)(584,699)
(585,700)(586,706)(587,707)(588,708)(589,709)(590,710)(591,716)(592,717)
(593,718)(594,719)(595,720)(596,711)(597,712)(598,713)(599,714)(600,715)
(721,841)(722,842)(723,843)(724,844)(725,845)(726,851)(727,852)(728,853)
(729,854)(730,855)(731,846)(732,847)(733,848)(734,849)(735,850)(736,856)
(737,857)(738,858)(739,859)(740,860)(741,866)(742,867)(743,868)(744,869)
(745,870)(746,861)(747,862)(748,863)(749,864)(750,865)(751,871)(752,872)
(753,873)(754,874)(755,875)(756,881)(757,882)(758,883)(759,884)(760,885)
(761,876)(762,877)(763,878)(764,879)(765,880)(766,886)(767,887)(768,888)
(769,889)(770,890)(771,896)(772,897)(773,898)(774,899)(775,900)(776,891)
(777,892)(778,893)(779,894)(780,895)(781,901)(782,902)(783,903)(784,904)
(785,905)(786,911)(787,912)(788,913)(789,914)(790,915)(791,906)(792,907)
(793,908)(794,909)(795,910)(796,916)(797,917)(798,918)(799,919)(800,920)
(801,926)(802,927)(803,928)(804,929)(805,930)(806,921)(807,922)(808,923)
(809,924)(810,925)(811,931)(812,932)(813,933)(814,934)(815,935)(816,941)
(817,942)(818,943)(819,944)(820,945)(821,936)(822,937)(823,938)(824,939)
(825,940)(826,946)(827,947)(828,948)(829,949)(830,950)(831,956)(832,957)
(833,958)(834,959)(835,960)(836,951)(837,952)(838,953)(839,954)(840,955);;
s1 := (  1,606)(  2,607)(  3,608)(  4,609)(  5,610)(  6,601)(  7,602)(  8,603)
(  9,604)( 10,605)( 11,611)( 12,612)( 13,613)( 14,614)( 15,615)( 16,621)
( 17,622)( 18,623)( 19,624)( 20,625)( 21,616)( 22,617)( 23,618)( 24,619)
( 25,620)( 26,626)( 27,627)( 28,628)( 29,629)( 30,630)( 31,636)( 32,637)
( 33,638)( 34,639)( 35,640)( 36,631)( 37,632)( 38,633)( 39,634)( 40,635)
( 41,641)( 42,642)( 43,643)( 44,644)( 45,645)( 46,651)( 47,652)( 48,653)
( 49,654)( 50,655)( 51,646)( 52,647)( 53,648)( 54,649)( 55,650)( 56,656)
( 57,657)( 58,658)( 59,659)( 60,660)( 61,681)( 62,682)( 63,683)( 64,684)
( 65,685)( 66,676)( 67,677)( 68,678)( 69,679)( 70,680)( 71,686)( 72,687)
( 73,688)( 74,689)( 75,690)( 76,666)( 77,667)( 78,668)( 79,669)( 80,670)
( 81,661)( 82,662)( 83,663)( 84,664)( 85,665)( 86,671)( 87,672)( 88,673)
( 89,674)( 90,675)( 91,711)( 92,712)( 93,713)( 94,714)( 95,715)( 96,706)
( 97,707)( 98,708)( 99,709)(100,710)(101,716)(102,717)(103,718)(104,719)
(105,720)(106,696)(107,697)(108,698)(109,699)(110,700)(111,691)(112,692)
(113,693)(114,694)(115,695)(116,701)(117,702)(118,703)(119,704)(120,705)
(121,486)(122,487)(123,488)(124,489)(125,490)(126,481)(127,482)(128,483)
(129,484)(130,485)(131,491)(132,492)(133,493)(134,494)(135,495)(136,501)
(137,502)(138,503)(139,504)(140,505)(141,496)(142,497)(143,498)(144,499)
(145,500)(146,506)(147,507)(148,508)(149,509)(150,510)(151,516)(152,517)
(153,518)(154,519)(155,520)(156,511)(157,512)(158,513)(159,514)(160,515)
(161,521)(162,522)(163,523)(164,524)(165,525)(166,531)(167,532)(168,533)
(169,534)(170,535)(171,526)(172,527)(173,528)(174,529)(175,530)(176,536)
(177,537)(178,538)(179,539)(180,540)(181,561)(182,562)(183,563)(184,564)
(185,565)(186,556)(187,557)(188,558)(189,559)(190,560)(191,566)(192,567)
(193,568)(194,569)(195,570)(196,546)(197,547)(198,548)(199,549)(200,550)
(201,541)(202,542)(203,543)(204,544)(205,545)(206,551)(207,552)(208,553)
(209,554)(210,555)(211,591)(212,592)(213,593)(214,594)(215,595)(216,586)
(217,587)(218,588)(219,589)(220,590)(221,596)(222,597)(223,598)(224,599)
(225,600)(226,576)(227,577)(228,578)(229,579)(230,580)(231,571)(232,572)
(233,573)(234,574)(235,575)(236,581)(237,582)(238,583)(239,584)(240,585)
(241,846)(242,847)(243,848)(244,849)(245,850)(246,841)(247,842)(248,843)
(249,844)(250,845)(251,851)(252,852)(253,853)(254,854)(255,855)(256,861)
(257,862)(258,863)(259,864)(260,865)(261,856)(262,857)(263,858)(264,859)
(265,860)(266,866)(267,867)(268,868)(269,869)(270,870)(271,876)(272,877)
(273,878)(274,879)(275,880)(276,871)(277,872)(278,873)(279,874)(280,875)
(281,881)(282,882)(283,883)(284,884)(285,885)(286,891)(287,892)(288,893)
(289,894)(290,895)(291,886)(292,887)(293,888)(294,889)(295,890)(296,896)
(297,897)(298,898)(299,899)(300,900)(301,921)(302,922)(303,923)(304,924)
(305,925)(306,916)(307,917)(308,918)(309,919)(310,920)(311,926)(312,927)
(313,928)(314,929)(315,930)(316,906)(317,907)(318,908)(319,909)(320,910)
(321,901)(322,902)(323,903)(324,904)(325,905)(326,911)(327,912)(328,913)
(329,914)(330,915)(331,951)(332,952)(333,953)(334,954)(335,955)(336,946)
(337,947)(338,948)(339,949)(340,950)(341,956)(342,957)(343,958)(344,959)
(345,960)(346,936)(347,937)(348,938)(349,939)(350,940)(351,931)(352,932)
(353,933)(354,934)(355,935)(356,941)(357,942)(358,943)(359,944)(360,945)
(361,726)(362,727)(363,728)(364,729)(365,730)(366,721)(367,722)(368,723)
(369,724)(370,725)(371,731)(372,732)(373,733)(374,734)(375,735)(376,741)
(377,742)(378,743)(379,744)(380,745)(381,736)(382,737)(383,738)(384,739)
(385,740)(386,746)(387,747)(388,748)(389,749)(390,750)(391,756)(392,757)
(393,758)(394,759)(395,760)(396,751)(397,752)(398,753)(399,754)(400,755)
(401,761)(402,762)(403,763)(404,764)(405,765)(406,771)(407,772)(408,773)
(409,774)(410,775)(411,766)(412,767)(413,768)(414,769)(415,770)(416,776)
(417,777)(418,778)(419,779)(420,780)(421,801)(422,802)(423,803)(424,804)
(425,805)(426,796)(427,797)(428,798)(429,799)(430,800)(431,806)(432,807)
(433,808)(434,809)(435,810)(436,786)(437,787)(438,788)(439,789)(440,790)
(441,781)(442,782)(443,783)(444,784)(445,785)(446,791)(447,792)(448,793)
(449,794)(450,795)(451,831)(452,832)(453,833)(454,834)(455,835)(456,826)
(457,827)(458,828)(459,829)(460,830)(461,836)(462,837)(463,838)(464,839)
(465,840)(466,816)(467,817)(468,818)(469,819)(470,820)(471,811)(472,812)
(473,813)(474,814)(475,815)(476,821)(477,822)(478,823)(479,824)(480,825);;
s2 := (  2,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)( 38, 39)
( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)( 58, 59)
( 61, 76)( 62, 80)( 63, 79)( 64, 78)( 65, 77)( 66, 81)( 67, 85)( 68, 84)
( 69, 83)( 70, 82)( 71, 86)( 72, 90)( 73, 89)( 74, 88)( 75, 87)( 91,106)
( 92,110)( 93,109)( 94,108)( 95,107)( 96,111)( 97,115)( 98,114)( 99,113)
(100,112)(101,116)(102,120)(103,119)(104,118)(105,117)(122,125)(123,124)
(127,130)(128,129)(132,135)(133,134)(137,140)(138,139)(142,145)(143,144)
(147,150)(148,149)(152,155)(153,154)(157,160)(158,159)(162,165)(163,164)
(167,170)(168,169)(172,175)(173,174)(177,180)(178,179)(181,196)(182,200)
(183,199)(184,198)(185,197)(186,201)(187,205)(188,204)(189,203)(190,202)
(191,206)(192,210)(193,209)(194,208)(195,207)(211,226)(212,230)(213,229)
(214,228)(215,227)(216,231)(217,235)(218,234)(219,233)(220,232)(221,236)
(222,240)(223,239)(224,238)(225,237)(241,271)(242,275)(243,274)(244,273)
(245,272)(246,276)(247,280)(248,279)(249,278)(250,277)(251,281)(252,285)
(253,284)(254,283)(255,282)(256,286)(257,290)(258,289)(259,288)(260,287)
(261,291)(262,295)(263,294)(264,293)(265,292)(266,296)(267,300)(268,299)
(269,298)(270,297)(301,346)(302,350)(303,349)(304,348)(305,347)(306,351)
(307,355)(308,354)(309,353)(310,352)(311,356)(312,360)(313,359)(314,358)
(315,357)(316,331)(317,335)(318,334)(319,333)(320,332)(321,336)(322,340)
(323,339)(324,338)(325,337)(326,341)(327,345)(328,344)(329,343)(330,342)
(361,391)(362,395)(363,394)(364,393)(365,392)(366,396)(367,400)(368,399)
(369,398)(370,397)(371,401)(372,405)(373,404)(374,403)(375,402)(376,406)
(377,410)(378,409)(379,408)(380,407)(381,411)(382,415)(383,414)(384,413)
(385,412)(386,416)(387,420)(388,419)(389,418)(390,417)(421,466)(422,470)
(423,469)(424,468)(425,467)(426,471)(427,475)(428,474)(429,473)(430,472)
(431,476)(432,480)(433,479)(434,478)(435,477)(436,451)(437,455)(438,454)
(439,453)(440,452)(441,456)(442,460)(443,459)(444,458)(445,457)(446,461)
(447,465)(448,464)(449,463)(450,462)(481,541)(482,545)(483,544)(484,543)
(485,542)(486,546)(487,550)(488,549)(489,548)(490,547)(491,551)(492,555)
(493,554)(494,553)(495,552)(496,556)(497,560)(498,559)(499,558)(500,557)
(501,561)(502,565)(503,564)(504,563)(505,562)(506,566)(507,570)(508,569)
(509,568)(510,567)(511,571)(512,575)(513,574)(514,573)(515,572)(516,576)
(517,580)(518,579)(519,578)(520,577)(521,581)(522,585)(523,584)(524,583)
(525,582)(526,586)(527,590)(528,589)(529,588)(530,587)(531,591)(532,595)
(533,594)(534,593)(535,592)(536,596)(537,600)(538,599)(539,598)(540,597)
(601,661)(602,665)(603,664)(604,663)(605,662)(606,666)(607,670)(608,669)
(609,668)(610,667)(611,671)(612,675)(613,674)(614,673)(615,672)(616,676)
(617,680)(618,679)(619,678)(620,677)(621,681)(622,685)(623,684)(624,683)
(625,682)(626,686)(627,690)(628,689)(629,688)(630,687)(631,691)(632,695)
(633,694)(634,693)(635,692)(636,696)(637,700)(638,699)(639,698)(640,697)
(641,701)(642,705)(643,704)(644,703)(645,702)(646,706)(647,710)(648,709)
(649,708)(650,707)(651,711)(652,715)(653,714)(654,713)(655,712)(656,716)
(657,720)(658,719)(659,718)(660,717)(721,811)(722,815)(723,814)(724,813)
(725,812)(726,816)(727,820)(728,819)(729,818)(730,817)(731,821)(732,825)
(733,824)(734,823)(735,822)(736,826)(737,830)(738,829)(739,828)(740,827)
(741,831)(742,835)(743,834)(744,833)(745,832)(746,836)(747,840)(748,839)
(749,838)(750,837)(751,781)(752,785)(753,784)(754,783)(755,782)(756,786)
(757,790)(758,789)(759,788)(760,787)(761,791)(762,795)(763,794)(764,793)
(765,792)(766,796)(767,800)(768,799)(769,798)(770,797)(771,801)(772,805)
(773,804)(774,803)(775,802)(776,806)(777,810)(778,809)(779,808)(780,807)
(841,931)(842,935)(843,934)(844,933)(845,932)(846,936)(847,940)(848,939)
(849,938)(850,937)(851,941)(852,945)(853,944)(854,943)(855,942)(856,946)
(857,950)(858,949)(859,948)(860,947)(861,951)(862,955)(863,954)(864,953)
(865,952)(866,956)(867,960)(868,959)(869,958)(870,957)(871,901)(872,905)
(873,904)(874,903)(875,902)(876,906)(877,910)(878,909)(879,908)(880,907)
(881,911)(882,915)(883,914)(884,913)(885,912)(886,916)(887,920)(888,919)
(889,918)(890,917)(891,921)(892,925)(893,924)(894,923)(895,922)(896,926)
(897,930)(898,929)(899,928)(900,927);;
s3 := (  1,242)(  2,241)(  3,245)(  4,244)(  5,243)(  6,247)(  7,246)(  8,250)
(  9,249)( 10,248)( 11,252)( 12,251)( 13,255)( 14,254)( 15,253)( 16,257)
( 17,256)( 18,260)( 19,259)( 20,258)( 21,262)( 22,261)( 23,265)( 24,264)
( 25,263)( 26,267)( 27,266)( 28,270)( 29,269)( 30,268)( 31,272)( 32,271)
( 33,275)( 34,274)( 35,273)( 36,277)( 37,276)( 38,280)( 39,279)( 40,278)
( 41,282)( 42,281)( 43,285)( 44,284)( 45,283)( 46,287)( 47,286)( 48,290)
( 49,289)( 50,288)( 51,292)( 52,291)( 53,295)( 54,294)( 55,293)( 56,297)
( 57,296)( 58,300)( 59,299)( 60,298)( 61,302)( 62,301)( 63,305)( 64,304)
( 65,303)( 66,307)( 67,306)( 68,310)( 69,309)( 70,308)( 71,312)( 72,311)
( 73,315)( 74,314)( 75,313)( 76,317)( 77,316)( 78,320)( 79,319)( 80,318)
( 81,322)( 82,321)( 83,325)( 84,324)( 85,323)( 86,327)( 87,326)( 88,330)
( 89,329)( 90,328)( 91,332)( 92,331)( 93,335)( 94,334)( 95,333)( 96,337)
( 97,336)( 98,340)( 99,339)(100,338)(101,342)(102,341)(103,345)(104,344)
(105,343)(106,347)(107,346)(108,350)(109,349)(110,348)(111,352)(112,351)
(113,355)(114,354)(115,353)(116,357)(117,356)(118,360)(119,359)(120,358)
(121,362)(122,361)(123,365)(124,364)(125,363)(126,367)(127,366)(128,370)
(129,369)(130,368)(131,372)(132,371)(133,375)(134,374)(135,373)(136,377)
(137,376)(138,380)(139,379)(140,378)(141,382)(142,381)(143,385)(144,384)
(145,383)(146,387)(147,386)(148,390)(149,389)(150,388)(151,392)(152,391)
(153,395)(154,394)(155,393)(156,397)(157,396)(158,400)(159,399)(160,398)
(161,402)(162,401)(163,405)(164,404)(165,403)(166,407)(167,406)(168,410)
(169,409)(170,408)(171,412)(172,411)(173,415)(174,414)(175,413)(176,417)
(177,416)(178,420)(179,419)(180,418)(181,422)(182,421)(183,425)(184,424)
(185,423)(186,427)(187,426)(188,430)(189,429)(190,428)(191,432)(192,431)
(193,435)(194,434)(195,433)(196,437)(197,436)(198,440)(199,439)(200,438)
(201,442)(202,441)(203,445)(204,444)(205,443)(206,447)(207,446)(208,450)
(209,449)(210,448)(211,452)(212,451)(213,455)(214,454)(215,453)(216,457)
(217,456)(218,460)(219,459)(220,458)(221,462)(222,461)(223,465)(224,464)
(225,463)(226,467)(227,466)(228,470)(229,469)(230,468)(231,472)(232,471)
(233,475)(234,474)(235,473)(236,477)(237,476)(238,480)(239,479)(240,478)
(481,722)(482,721)(483,725)(484,724)(485,723)(486,727)(487,726)(488,730)
(489,729)(490,728)(491,732)(492,731)(493,735)(494,734)(495,733)(496,737)
(497,736)(498,740)(499,739)(500,738)(501,742)(502,741)(503,745)(504,744)
(505,743)(506,747)(507,746)(508,750)(509,749)(510,748)(511,752)(512,751)
(513,755)(514,754)(515,753)(516,757)(517,756)(518,760)(519,759)(520,758)
(521,762)(522,761)(523,765)(524,764)(525,763)(526,767)(527,766)(528,770)
(529,769)(530,768)(531,772)(532,771)(533,775)(534,774)(535,773)(536,777)
(537,776)(538,780)(539,779)(540,778)(541,782)(542,781)(543,785)(544,784)
(545,783)(546,787)(547,786)(548,790)(549,789)(550,788)(551,792)(552,791)
(553,795)(554,794)(555,793)(556,797)(557,796)(558,800)(559,799)(560,798)
(561,802)(562,801)(563,805)(564,804)(565,803)(566,807)(567,806)(568,810)
(569,809)(570,808)(571,812)(572,811)(573,815)(574,814)(575,813)(576,817)
(577,816)(578,820)(579,819)(580,818)(581,822)(582,821)(583,825)(584,824)
(585,823)(586,827)(587,826)(588,830)(589,829)(590,828)(591,832)(592,831)
(593,835)(594,834)(595,833)(596,837)(597,836)(598,840)(599,839)(600,838)
(601,842)(602,841)(603,845)(604,844)(605,843)(606,847)(607,846)(608,850)
(609,849)(610,848)(611,852)(612,851)(613,855)(614,854)(615,853)(616,857)
(617,856)(618,860)(619,859)(620,858)(621,862)(622,861)(623,865)(624,864)
(625,863)(626,867)(627,866)(628,870)(629,869)(630,868)(631,872)(632,871)
(633,875)(634,874)(635,873)(636,877)(637,876)(638,880)(639,879)(640,878)
(641,882)(642,881)(643,885)(644,884)(645,883)(646,887)(647,886)(648,890)
(649,889)(650,888)(651,892)(652,891)(653,895)(654,894)(655,893)(656,897)
(657,896)(658,900)(659,899)(660,898)(661,902)(662,901)(663,905)(664,904)
(665,903)(666,907)(667,906)(668,910)(669,909)(670,908)(671,912)(672,911)
(673,915)(674,914)(675,913)(676,917)(677,916)(678,920)(679,919)(680,918)
(681,922)(682,921)(683,925)(684,924)(685,923)(686,927)(687,926)(688,930)
(689,929)(690,928)(691,932)(692,931)(693,935)(694,934)(695,933)(696,937)
(697,936)(698,940)(699,939)(700,938)(701,942)(702,941)(703,945)(704,944)
(705,943)(706,947)(707,946)(708,950)(709,949)(710,948)(711,952)(712,951)
(713,955)(714,954)(715,953)(716,957)(717,956)(718,960)(719,959)(720,958);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) : 
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(960)!(  1,121)(  2,122)(  3,123)(  4,124)(  5,125)(  6,131)(  7,132)
(  8,133)(  9,134)( 10,135)( 11,126)( 12,127)( 13,128)( 14,129)( 15,130)
( 16,136)( 17,137)( 18,138)( 19,139)( 20,140)( 21,146)( 22,147)( 23,148)
( 24,149)( 25,150)( 26,141)( 27,142)( 28,143)( 29,144)( 30,145)( 31,151)
( 32,152)( 33,153)( 34,154)( 35,155)( 36,161)( 37,162)( 38,163)( 39,164)
( 40,165)( 41,156)( 42,157)( 43,158)( 44,159)( 45,160)( 46,166)( 47,167)
( 48,168)( 49,169)( 50,170)( 51,176)( 52,177)( 53,178)( 54,179)( 55,180)
( 56,171)( 57,172)( 58,173)( 59,174)( 60,175)( 61,181)( 62,182)( 63,183)
( 64,184)( 65,185)( 66,191)( 67,192)( 68,193)( 69,194)( 70,195)( 71,186)
( 72,187)( 73,188)( 74,189)( 75,190)( 76,196)( 77,197)( 78,198)( 79,199)
( 80,200)( 81,206)( 82,207)( 83,208)( 84,209)( 85,210)( 86,201)( 87,202)
( 88,203)( 89,204)( 90,205)( 91,211)( 92,212)( 93,213)( 94,214)( 95,215)
( 96,221)( 97,222)( 98,223)( 99,224)(100,225)(101,216)(102,217)(103,218)
(104,219)(105,220)(106,226)(107,227)(108,228)(109,229)(110,230)(111,236)
(112,237)(113,238)(114,239)(115,240)(116,231)(117,232)(118,233)(119,234)
(120,235)(241,361)(242,362)(243,363)(244,364)(245,365)(246,371)(247,372)
(248,373)(249,374)(250,375)(251,366)(252,367)(253,368)(254,369)(255,370)
(256,376)(257,377)(258,378)(259,379)(260,380)(261,386)(262,387)(263,388)
(264,389)(265,390)(266,381)(267,382)(268,383)(269,384)(270,385)(271,391)
(272,392)(273,393)(274,394)(275,395)(276,401)(277,402)(278,403)(279,404)
(280,405)(281,396)(282,397)(283,398)(284,399)(285,400)(286,406)(287,407)
(288,408)(289,409)(290,410)(291,416)(292,417)(293,418)(294,419)(295,420)
(296,411)(297,412)(298,413)(299,414)(300,415)(301,421)(302,422)(303,423)
(304,424)(305,425)(306,431)(307,432)(308,433)(309,434)(310,435)(311,426)
(312,427)(313,428)(314,429)(315,430)(316,436)(317,437)(318,438)(319,439)
(320,440)(321,446)(322,447)(323,448)(324,449)(325,450)(326,441)(327,442)
(328,443)(329,444)(330,445)(331,451)(332,452)(333,453)(334,454)(335,455)
(336,461)(337,462)(338,463)(339,464)(340,465)(341,456)(342,457)(343,458)
(344,459)(345,460)(346,466)(347,467)(348,468)(349,469)(350,470)(351,476)
(352,477)(353,478)(354,479)(355,480)(356,471)(357,472)(358,473)(359,474)
(360,475)(481,601)(482,602)(483,603)(484,604)(485,605)(486,611)(487,612)
(488,613)(489,614)(490,615)(491,606)(492,607)(493,608)(494,609)(495,610)
(496,616)(497,617)(498,618)(499,619)(500,620)(501,626)(502,627)(503,628)
(504,629)(505,630)(506,621)(507,622)(508,623)(509,624)(510,625)(511,631)
(512,632)(513,633)(514,634)(515,635)(516,641)(517,642)(518,643)(519,644)
(520,645)(521,636)(522,637)(523,638)(524,639)(525,640)(526,646)(527,647)
(528,648)(529,649)(530,650)(531,656)(532,657)(533,658)(534,659)(535,660)
(536,651)(537,652)(538,653)(539,654)(540,655)(541,661)(542,662)(543,663)
(544,664)(545,665)(546,671)(547,672)(548,673)(549,674)(550,675)(551,666)
(552,667)(553,668)(554,669)(555,670)(556,676)(557,677)(558,678)(559,679)
(560,680)(561,686)(562,687)(563,688)(564,689)(565,690)(566,681)(567,682)
(568,683)(569,684)(570,685)(571,691)(572,692)(573,693)(574,694)(575,695)
(576,701)(577,702)(578,703)(579,704)(580,705)(581,696)(582,697)(583,698)
(584,699)(585,700)(586,706)(587,707)(588,708)(589,709)(590,710)(591,716)
(592,717)(593,718)(594,719)(595,720)(596,711)(597,712)(598,713)(599,714)
(600,715)(721,841)(722,842)(723,843)(724,844)(725,845)(726,851)(727,852)
(728,853)(729,854)(730,855)(731,846)(732,847)(733,848)(734,849)(735,850)
(736,856)(737,857)(738,858)(739,859)(740,860)(741,866)(742,867)(743,868)
(744,869)(745,870)(746,861)(747,862)(748,863)(749,864)(750,865)(751,871)
(752,872)(753,873)(754,874)(755,875)(756,881)(757,882)(758,883)(759,884)
(760,885)(761,876)(762,877)(763,878)(764,879)(765,880)(766,886)(767,887)
(768,888)(769,889)(770,890)(771,896)(772,897)(773,898)(774,899)(775,900)
(776,891)(777,892)(778,893)(779,894)(780,895)(781,901)(782,902)(783,903)
(784,904)(785,905)(786,911)(787,912)(788,913)(789,914)(790,915)(791,906)
(792,907)(793,908)(794,909)(795,910)(796,916)(797,917)(798,918)(799,919)
(800,920)(801,926)(802,927)(803,928)(804,929)(805,930)(806,921)(807,922)
(808,923)(809,924)(810,925)(811,931)(812,932)(813,933)(814,934)(815,935)
(816,941)(817,942)(818,943)(819,944)(820,945)(821,936)(822,937)(823,938)
(824,939)(825,940)(826,946)(827,947)(828,948)(829,949)(830,950)(831,956)
(832,957)(833,958)(834,959)(835,960)(836,951)(837,952)(838,953)(839,954)
(840,955);
s1 := Sym(960)!(  1,606)(  2,607)(  3,608)(  4,609)(  5,610)(  6,601)(  7,602)
(  8,603)(  9,604)( 10,605)( 11,611)( 12,612)( 13,613)( 14,614)( 15,615)
( 16,621)( 17,622)( 18,623)( 19,624)( 20,625)( 21,616)( 22,617)( 23,618)
( 24,619)( 25,620)( 26,626)( 27,627)( 28,628)( 29,629)( 30,630)( 31,636)
( 32,637)( 33,638)( 34,639)( 35,640)( 36,631)( 37,632)( 38,633)( 39,634)
( 40,635)( 41,641)( 42,642)( 43,643)( 44,644)( 45,645)( 46,651)( 47,652)
( 48,653)( 49,654)( 50,655)( 51,646)( 52,647)( 53,648)( 54,649)( 55,650)
( 56,656)( 57,657)( 58,658)( 59,659)( 60,660)( 61,681)( 62,682)( 63,683)
( 64,684)( 65,685)( 66,676)( 67,677)( 68,678)( 69,679)( 70,680)( 71,686)
( 72,687)( 73,688)( 74,689)( 75,690)( 76,666)( 77,667)( 78,668)( 79,669)
( 80,670)( 81,661)( 82,662)( 83,663)( 84,664)( 85,665)( 86,671)( 87,672)
( 88,673)( 89,674)( 90,675)( 91,711)( 92,712)( 93,713)( 94,714)( 95,715)
( 96,706)( 97,707)( 98,708)( 99,709)(100,710)(101,716)(102,717)(103,718)
(104,719)(105,720)(106,696)(107,697)(108,698)(109,699)(110,700)(111,691)
(112,692)(113,693)(114,694)(115,695)(116,701)(117,702)(118,703)(119,704)
(120,705)(121,486)(122,487)(123,488)(124,489)(125,490)(126,481)(127,482)
(128,483)(129,484)(130,485)(131,491)(132,492)(133,493)(134,494)(135,495)
(136,501)(137,502)(138,503)(139,504)(140,505)(141,496)(142,497)(143,498)
(144,499)(145,500)(146,506)(147,507)(148,508)(149,509)(150,510)(151,516)
(152,517)(153,518)(154,519)(155,520)(156,511)(157,512)(158,513)(159,514)
(160,515)(161,521)(162,522)(163,523)(164,524)(165,525)(166,531)(167,532)
(168,533)(169,534)(170,535)(171,526)(172,527)(173,528)(174,529)(175,530)
(176,536)(177,537)(178,538)(179,539)(180,540)(181,561)(182,562)(183,563)
(184,564)(185,565)(186,556)(187,557)(188,558)(189,559)(190,560)(191,566)
(192,567)(193,568)(194,569)(195,570)(196,546)(197,547)(198,548)(199,549)
(200,550)(201,541)(202,542)(203,543)(204,544)(205,545)(206,551)(207,552)
(208,553)(209,554)(210,555)(211,591)(212,592)(213,593)(214,594)(215,595)
(216,586)(217,587)(218,588)(219,589)(220,590)(221,596)(222,597)(223,598)
(224,599)(225,600)(226,576)(227,577)(228,578)(229,579)(230,580)(231,571)
(232,572)(233,573)(234,574)(235,575)(236,581)(237,582)(238,583)(239,584)
(240,585)(241,846)(242,847)(243,848)(244,849)(245,850)(246,841)(247,842)
(248,843)(249,844)(250,845)(251,851)(252,852)(253,853)(254,854)(255,855)
(256,861)(257,862)(258,863)(259,864)(260,865)(261,856)(262,857)(263,858)
(264,859)(265,860)(266,866)(267,867)(268,868)(269,869)(270,870)(271,876)
(272,877)(273,878)(274,879)(275,880)(276,871)(277,872)(278,873)(279,874)
(280,875)(281,881)(282,882)(283,883)(284,884)(285,885)(286,891)(287,892)
(288,893)(289,894)(290,895)(291,886)(292,887)(293,888)(294,889)(295,890)
(296,896)(297,897)(298,898)(299,899)(300,900)(301,921)(302,922)(303,923)
(304,924)(305,925)(306,916)(307,917)(308,918)(309,919)(310,920)(311,926)
(312,927)(313,928)(314,929)(315,930)(316,906)(317,907)(318,908)(319,909)
(320,910)(321,901)(322,902)(323,903)(324,904)(325,905)(326,911)(327,912)
(328,913)(329,914)(330,915)(331,951)(332,952)(333,953)(334,954)(335,955)
(336,946)(337,947)(338,948)(339,949)(340,950)(341,956)(342,957)(343,958)
(344,959)(345,960)(346,936)(347,937)(348,938)(349,939)(350,940)(351,931)
(352,932)(353,933)(354,934)(355,935)(356,941)(357,942)(358,943)(359,944)
(360,945)(361,726)(362,727)(363,728)(364,729)(365,730)(366,721)(367,722)
(368,723)(369,724)(370,725)(371,731)(372,732)(373,733)(374,734)(375,735)
(376,741)(377,742)(378,743)(379,744)(380,745)(381,736)(382,737)(383,738)
(384,739)(385,740)(386,746)(387,747)(388,748)(389,749)(390,750)(391,756)
(392,757)(393,758)(394,759)(395,760)(396,751)(397,752)(398,753)(399,754)
(400,755)(401,761)(402,762)(403,763)(404,764)(405,765)(406,771)(407,772)
(408,773)(409,774)(410,775)(411,766)(412,767)(413,768)(414,769)(415,770)
(416,776)(417,777)(418,778)(419,779)(420,780)(421,801)(422,802)(423,803)
(424,804)(425,805)(426,796)(427,797)(428,798)(429,799)(430,800)(431,806)
(432,807)(433,808)(434,809)(435,810)(436,786)(437,787)(438,788)(439,789)
(440,790)(441,781)(442,782)(443,783)(444,784)(445,785)(446,791)(447,792)
(448,793)(449,794)(450,795)(451,831)(452,832)(453,833)(454,834)(455,835)
(456,826)(457,827)(458,828)(459,829)(460,830)(461,836)(462,837)(463,838)
(464,839)(465,840)(466,816)(467,817)(468,818)(469,819)(470,820)(471,811)
(472,812)(473,813)(474,814)(475,815)(476,821)(477,822)(478,823)(479,824)
(480,825);
s2 := Sym(960)!(  2,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)
( 38, 39)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)
( 58, 59)( 61, 76)( 62, 80)( 63, 79)( 64, 78)( 65, 77)( 66, 81)( 67, 85)
( 68, 84)( 69, 83)( 70, 82)( 71, 86)( 72, 90)( 73, 89)( 74, 88)( 75, 87)
( 91,106)( 92,110)( 93,109)( 94,108)( 95,107)( 96,111)( 97,115)( 98,114)
( 99,113)(100,112)(101,116)(102,120)(103,119)(104,118)(105,117)(122,125)
(123,124)(127,130)(128,129)(132,135)(133,134)(137,140)(138,139)(142,145)
(143,144)(147,150)(148,149)(152,155)(153,154)(157,160)(158,159)(162,165)
(163,164)(167,170)(168,169)(172,175)(173,174)(177,180)(178,179)(181,196)
(182,200)(183,199)(184,198)(185,197)(186,201)(187,205)(188,204)(189,203)
(190,202)(191,206)(192,210)(193,209)(194,208)(195,207)(211,226)(212,230)
(213,229)(214,228)(215,227)(216,231)(217,235)(218,234)(219,233)(220,232)
(221,236)(222,240)(223,239)(224,238)(225,237)(241,271)(242,275)(243,274)
(244,273)(245,272)(246,276)(247,280)(248,279)(249,278)(250,277)(251,281)
(252,285)(253,284)(254,283)(255,282)(256,286)(257,290)(258,289)(259,288)
(260,287)(261,291)(262,295)(263,294)(264,293)(265,292)(266,296)(267,300)
(268,299)(269,298)(270,297)(301,346)(302,350)(303,349)(304,348)(305,347)
(306,351)(307,355)(308,354)(309,353)(310,352)(311,356)(312,360)(313,359)
(314,358)(315,357)(316,331)(317,335)(318,334)(319,333)(320,332)(321,336)
(322,340)(323,339)(324,338)(325,337)(326,341)(327,345)(328,344)(329,343)
(330,342)(361,391)(362,395)(363,394)(364,393)(365,392)(366,396)(367,400)
(368,399)(369,398)(370,397)(371,401)(372,405)(373,404)(374,403)(375,402)
(376,406)(377,410)(378,409)(379,408)(380,407)(381,411)(382,415)(383,414)
(384,413)(385,412)(386,416)(387,420)(388,419)(389,418)(390,417)(421,466)
(422,470)(423,469)(424,468)(425,467)(426,471)(427,475)(428,474)(429,473)
(430,472)(431,476)(432,480)(433,479)(434,478)(435,477)(436,451)(437,455)
(438,454)(439,453)(440,452)(441,456)(442,460)(443,459)(444,458)(445,457)
(446,461)(447,465)(448,464)(449,463)(450,462)(481,541)(482,545)(483,544)
(484,543)(485,542)(486,546)(487,550)(488,549)(489,548)(490,547)(491,551)
(492,555)(493,554)(494,553)(495,552)(496,556)(497,560)(498,559)(499,558)
(500,557)(501,561)(502,565)(503,564)(504,563)(505,562)(506,566)(507,570)
(508,569)(509,568)(510,567)(511,571)(512,575)(513,574)(514,573)(515,572)
(516,576)(517,580)(518,579)(519,578)(520,577)(521,581)(522,585)(523,584)
(524,583)(525,582)(526,586)(527,590)(528,589)(529,588)(530,587)(531,591)
(532,595)(533,594)(534,593)(535,592)(536,596)(537,600)(538,599)(539,598)
(540,597)(601,661)(602,665)(603,664)(604,663)(605,662)(606,666)(607,670)
(608,669)(609,668)(610,667)(611,671)(612,675)(613,674)(614,673)(615,672)
(616,676)(617,680)(618,679)(619,678)(620,677)(621,681)(622,685)(623,684)
(624,683)(625,682)(626,686)(627,690)(628,689)(629,688)(630,687)(631,691)
(632,695)(633,694)(634,693)(635,692)(636,696)(637,700)(638,699)(639,698)
(640,697)(641,701)(642,705)(643,704)(644,703)(645,702)(646,706)(647,710)
(648,709)(649,708)(650,707)(651,711)(652,715)(653,714)(654,713)(655,712)
(656,716)(657,720)(658,719)(659,718)(660,717)(721,811)(722,815)(723,814)
(724,813)(725,812)(726,816)(727,820)(728,819)(729,818)(730,817)(731,821)
(732,825)(733,824)(734,823)(735,822)(736,826)(737,830)(738,829)(739,828)
(740,827)(741,831)(742,835)(743,834)(744,833)(745,832)(746,836)(747,840)
(748,839)(749,838)(750,837)(751,781)(752,785)(753,784)(754,783)(755,782)
(756,786)(757,790)(758,789)(759,788)(760,787)(761,791)(762,795)(763,794)
(764,793)(765,792)(766,796)(767,800)(768,799)(769,798)(770,797)(771,801)
(772,805)(773,804)(774,803)(775,802)(776,806)(777,810)(778,809)(779,808)
(780,807)(841,931)(842,935)(843,934)(844,933)(845,932)(846,936)(847,940)
(848,939)(849,938)(850,937)(851,941)(852,945)(853,944)(854,943)(855,942)
(856,946)(857,950)(858,949)(859,948)(860,947)(861,951)(862,955)(863,954)
(864,953)(865,952)(866,956)(867,960)(868,959)(869,958)(870,957)(871,901)
(872,905)(873,904)(874,903)(875,902)(876,906)(877,910)(878,909)(879,908)
(880,907)(881,911)(882,915)(883,914)(884,913)(885,912)(886,916)(887,920)
(888,919)(889,918)(890,917)(891,921)(892,925)(893,924)(894,923)(895,922)
(896,926)(897,930)(898,929)(899,928)(900,927);
s3 := Sym(960)!(  1,242)(  2,241)(  3,245)(  4,244)(  5,243)(  6,247)(  7,246)
(  8,250)(  9,249)( 10,248)( 11,252)( 12,251)( 13,255)( 14,254)( 15,253)
( 16,257)( 17,256)( 18,260)( 19,259)( 20,258)( 21,262)( 22,261)( 23,265)
( 24,264)( 25,263)( 26,267)( 27,266)( 28,270)( 29,269)( 30,268)( 31,272)
( 32,271)( 33,275)( 34,274)( 35,273)( 36,277)( 37,276)( 38,280)( 39,279)
( 40,278)( 41,282)( 42,281)( 43,285)( 44,284)( 45,283)( 46,287)( 47,286)
( 48,290)( 49,289)( 50,288)( 51,292)( 52,291)( 53,295)( 54,294)( 55,293)
( 56,297)( 57,296)( 58,300)( 59,299)( 60,298)( 61,302)( 62,301)( 63,305)
( 64,304)( 65,303)( 66,307)( 67,306)( 68,310)( 69,309)( 70,308)( 71,312)
( 72,311)( 73,315)( 74,314)( 75,313)( 76,317)( 77,316)( 78,320)( 79,319)
( 80,318)( 81,322)( 82,321)( 83,325)( 84,324)( 85,323)( 86,327)( 87,326)
( 88,330)( 89,329)( 90,328)( 91,332)( 92,331)( 93,335)( 94,334)( 95,333)
( 96,337)( 97,336)( 98,340)( 99,339)(100,338)(101,342)(102,341)(103,345)
(104,344)(105,343)(106,347)(107,346)(108,350)(109,349)(110,348)(111,352)
(112,351)(113,355)(114,354)(115,353)(116,357)(117,356)(118,360)(119,359)
(120,358)(121,362)(122,361)(123,365)(124,364)(125,363)(126,367)(127,366)
(128,370)(129,369)(130,368)(131,372)(132,371)(133,375)(134,374)(135,373)
(136,377)(137,376)(138,380)(139,379)(140,378)(141,382)(142,381)(143,385)
(144,384)(145,383)(146,387)(147,386)(148,390)(149,389)(150,388)(151,392)
(152,391)(153,395)(154,394)(155,393)(156,397)(157,396)(158,400)(159,399)
(160,398)(161,402)(162,401)(163,405)(164,404)(165,403)(166,407)(167,406)
(168,410)(169,409)(170,408)(171,412)(172,411)(173,415)(174,414)(175,413)
(176,417)(177,416)(178,420)(179,419)(180,418)(181,422)(182,421)(183,425)
(184,424)(185,423)(186,427)(187,426)(188,430)(189,429)(190,428)(191,432)
(192,431)(193,435)(194,434)(195,433)(196,437)(197,436)(198,440)(199,439)
(200,438)(201,442)(202,441)(203,445)(204,444)(205,443)(206,447)(207,446)
(208,450)(209,449)(210,448)(211,452)(212,451)(213,455)(214,454)(215,453)
(216,457)(217,456)(218,460)(219,459)(220,458)(221,462)(222,461)(223,465)
(224,464)(225,463)(226,467)(227,466)(228,470)(229,469)(230,468)(231,472)
(232,471)(233,475)(234,474)(235,473)(236,477)(237,476)(238,480)(239,479)
(240,478)(481,722)(482,721)(483,725)(484,724)(485,723)(486,727)(487,726)
(488,730)(489,729)(490,728)(491,732)(492,731)(493,735)(494,734)(495,733)
(496,737)(497,736)(498,740)(499,739)(500,738)(501,742)(502,741)(503,745)
(504,744)(505,743)(506,747)(507,746)(508,750)(509,749)(510,748)(511,752)
(512,751)(513,755)(514,754)(515,753)(516,757)(517,756)(518,760)(519,759)
(520,758)(521,762)(522,761)(523,765)(524,764)(525,763)(526,767)(527,766)
(528,770)(529,769)(530,768)(531,772)(532,771)(533,775)(534,774)(535,773)
(536,777)(537,776)(538,780)(539,779)(540,778)(541,782)(542,781)(543,785)
(544,784)(545,783)(546,787)(547,786)(548,790)(549,789)(550,788)(551,792)
(552,791)(553,795)(554,794)(555,793)(556,797)(557,796)(558,800)(559,799)
(560,798)(561,802)(562,801)(563,805)(564,804)(565,803)(566,807)(567,806)
(568,810)(569,809)(570,808)(571,812)(572,811)(573,815)(574,814)(575,813)
(576,817)(577,816)(578,820)(579,819)(580,818)(581,822)(582,821)(583,825)
(584,824)(585,823)(586,827)(587,826)(588,830)(589,829)(590,828)(591,832)
(592,831)(593,835)(594,834)(595,833)(596,837)(597,836)(598,840)(599,839)
(600,838)(601,842)(602,841)(603,845)(604,844)(605,843)(606,847)(607,846)
(608,850)(609,849)(610,848)(611,852)(612,851)(613,855)(614,854)(615,853)
(616,857)(617,856)(618,860)(619,859)(620,858)(621,862)(622,861)(623,865)
(624,864)(625,863)(626,867)(627,866)(628,870)(629,869)(630,868)(631,872)
(632,871)(633,875)(634,874)(635,873)(636,877)(637,876)(638,880)(639,879)
(640,878)(641,882)(642,881)(643,885)(644,884)(645,883)(646,887)(647,886)
(648,890)(649,889)(650,888)(651,892)(652,891)(653,895)(654,894)(655,893)
(656,897)(657,896)(658,900)(659,899)(660,898)(661,902)(662,901)(663,905)
(664,904)(665,903)(666,907)(667,906)(668,910)(669,909)(670,908)(671,912)
(672,911)(673,915)(674,914)(675,913)(676,917)(677,916)(678,920)(679,919)
(680,918)(681,922)(682,921)(683,925)(684,924)(685,923)(686,927)(687,926)
(688,930)(689,929)(690,928)(691,932)(692,931)(693,935)(694,934)(695,933)
(696,937)(697,936)(698,940)(699,939)(700,938)(701,942)(702,941)(703,945)
(704,944)(705,943)(706,947)(707,946)(708,950)(709,949)(710,948)(711,952)
(712,951)(713,955)(714,954)(715,953)(716,957)(717,956)(718,960)(719,959)
(720,958);
poly := sub<Sym(960)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) : 
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope